For all pairs $(M,L)$ satisfying the property that $M\setminus L$ is homeomorphic to some underlying shadow link complement, the relative Reshetikhin-Turaev We study the asymptotic expansion conjecture of the invariants. Such a hyperbolic conic structure of $(M,L)$ can be described using some basic shadow-link meridian logarithmic holonomies. If the log holonomy is sufficiently small that all cone angles are less than $\pi$, then the asymptotic expansion conjecture for $(M,L)$ is true. In particular, the relative Reshetikhin-Turaev invariants for all pairs $(M,L)$ that satisfy the property that the cone angle is sufficiently small and that $M\setminus L$ is homeomorphic to some underlying shadow link complement. Verify the asymptotic expansion conjecture of . Furthermore, we show that the cone angle can be pushed to any value below $\pi$ if $M$ can be obtained by doing reasonable surgery on the underlying shadow link complement with a sufficiently large surgery coefficient. indicate.